TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantization and boundary value problems
JF  - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology
N2  - We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.
KW  - Symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2016
U6  - https://doi.org/10.1142/S0219887816500079
SN  - 0219-8878
SN  - 1793-6977
VL  - 13
SP  - 176
EP  - 195
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantisation and boundary value problems
N2  - We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 5 
KW  - symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77150
SN  - 2193-6943
VL  - 4
IS  - 5
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A spectral theorem for deformation quantisation
N2  - We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 4 
KW  - star product
KW  - WKB method
KW  - spectral theorem
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-72425
SN  - 2193-6943
VL  - 4
IS  - 4
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On index theorem for symplectic orbifolds
N2  - We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.
T3  - Preprint - (2003) 07 
KW  - star product
KW  - symmetry group
KW  - G-trace
KW  - G-index
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26550
ER  -